28
The coordinate line. Showing positive and negative numbers on the number line
Textbook, pp. 127–131
GoalKnow the coordinate line; show positive and negative numbers on it and read a point's coordinate.
New words
coordinate line (number line) · koordinata to‘g‘ri chizig‘iorigin · koordinata boshiunit segment · birlik kesmacoordinate of a point · nuqta koordinatasi
Explanation
The coordinate line is a straight line with a chosen starting point (the origin O), a direction and a unit segment. Usually the direction is to the right. Positive numbers lie to the right of O and negative numbers to the left. Each point corresponds to exactly one number, its coordinate: A(−3) means the coordinate of point A is −3. The unit segments must all be the same length. The distance between two points is found by counting the unit segments between them.
Worked examples
The distance between A(−3) and B(2): from A to O is 3 units, from O to B is 2 units, so 3 + 2 = 5 units.
The midpoint of −6 and 2: the distance between them is 6 + 2 = 8 units, half of it is 4; moving 4 units left from 2 we reach −2, which is 4 units from both −6 and 2.
Class activity
“Human number line”: a number line from −5 to 5 is chalked on the floor. One pupil stands as a “point” and others give orders like “A(−3)” for the pupil to step to the right place.
Practice
1
On which side of the origin do positive numbers lie?
On the right
2
How many units are between A(−4) and B(3)?
7
3
Find the number halfway between −6 and 2.
-2
4
Why must the unit segments on a number line all have the same length?
Otherwise distances would not show the true difference and we could not compare numbers.